Properties

Label 175.4.n
Level $175$
Weight $4$
Character orbit 175.n
Rep. character $\chi_{175}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $184$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 175.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(175, [\chi])\).

Total New Old
Modular forms 248 184 64
Cusp forms 232 184 48
Eisenstein series 16 0 16

Trace form

\( 184 q + 192 q^{4} - 46 q^{5} + 386 q^{9} + 16 q^{10} - 88 q^{11} + 320 q^{12} + 56 q^{14} + 212 q^{15} - 1048 q^{16} + 72 q^{19} - 732 q^{20} - 84 q^{21} + 290 q^{22} - 220 q^{23} - 28 q^{24} - 838 q^{25}+ \cdots - 7920 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.4.n.a 175.n 25.e $184$ $10.325$ None 175.4.n.a \(0\) \(0\) \(-46\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{4}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(175, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)